How do I compute log-likelihood for training set in supervised learning?
The log-likelihood function for the training set (in general, not for deep learning in particular) will depend on your choice of loss function.

I'm guessing you're using something like a quadratic loss function for a binary classification problem, since this is a common approach. In that case, the log-likelihood is the sum of logs of the squared differences between the target label and the softmax value produced by your model. If you want to compute the log likelihood under a particular set of parameters (say, those that minimize validation error), then you just use those parameters in the model when generating softmax values.